The Hilbert transform as been investigated abundantly in coherent imaging. To the best of our knowledge, it is for the first time investigated in the context of incoherent imaging. We present a two-pupil optical heterodyne scanning system and analyze mathematically the design of its two pupils such that the optical system can perform the Hilbert transform on incoherent objects. Computer simulations of the idea clarify the theoretical results. (c) 2007 Optical Society of America.